L-functions with n-th order twists

Valentin Blomer; Leo Goldmakher; Benoit Louvel

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arXiv · 1112.1650

L-functions with n-th order twists

Valentin Blomer·Leo Goldmakher·Benoit Louvel

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Abstract

Let K be a number field containing the n-th roots of unity for some n > 2. We prove a uniform subconvexity result for a family of double Dirichlet series built out of central values of Hecke L-functions of n-th order characters of K. The main new ingredient, possibly of independent interest, is a large sieve for n-th order characters. As further applications of this tool, we derive several results concerning L(s,χ) for n-th order Hecke characters: an estimate of the second moment on the critical line, a non-vanishing result at the central point, and a zero-density theorem.

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Valentin Blomer, Leo Goldmakher, Benoit Louvel. 2011-12-07. L-functions with n-th order twists. https://arxiv.org/abs/1112.1650

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